(a)0.05.
(b)0.025.
(c)0.20.3.11 Verify the numbers in the first two rows of Table 3.10 in Example 3.8;
for example, show that the lowest healthy systolic blood pressure for 16-
year-old boys is 102.8.
3.12 Complete Table 3.10 in Example 3.8 at the question marks.
3.13 Medical research has concluded that people experience a common cold
roughly two times per year. Assume that the time between colds is nor-
mally distributed with a mean of 160 days and a standard deviation of
40 days.
(a)What is the probability of going 200 or more days between colds? Of
going 365 or more days?
(b)What is the probability of getting a cold within 80 days of a previous
cold?
3.14 Assume that the test scores for a large class are normally distributed with
a mean of 74 and a standard deviation of 10.
(a)Suppose that you receive a score of 88. What percent of the class
received scores higher than yours?
(b)Suppose that the teacher wants to limit the number of A grades in
the class to no more than 20%. What would be the lowest score for
an A?
3.15 Intelligence test scores, referred to asintelligence quotientor IQ scores,
are based on characteristics such as verbal skills, abstract reasoning
power, numerical ability, and spatial visualization. If plotted on a graph,
the distribution of IQ scores approximates a normal curve with a mean
of about 100. An IQ score above 115 is considered superior. Studies of
‘‘intellectually gifted’’ children have generally defined the lower limit of
their IQ scores at 140; approximately 1% of the population have IQ
scores above this limit. (Based on Biracree, 1984.)
(a)Find the standard deviation of this distribution.
(b)What percent are in the ‘‘superior’’ range of 115 or above?
(c)What percent of the population have IQ scores of 70 or below?
3.16 IQ scores for college graduates are normally distributed with a mean of
120 (as compared to 100 for the general population) with a standard
deviation of 12. What is the probability of randomly selecting a graduate
student with an IQ score:
(a)Between 110 and 130?
(b)Above 140?
(c)Below 100?
144 PROBABILITY AND PROBABILITY MODELS